250 REPORT— 1876. 



bounding interface separating the region' of flow with important energy of 

 motion from the region which may be regarded as statical, or as devoid of 

 important energy of motion. Let U' U U" be another interface crossing the 

 stream-lines at any place in the region of flow. 



Now taking as the unit of volume the cube of the unit of length, taking 

 as the unit of area the square of the unit of length, taking the unit of 

 density as unit of mass per unit of volume, so that the density of a body 

 will be the number of units of mass per unit of volume, taking as the unit 

 of force the force which acting on a unit of mass for a unit of time 

 imparts to it a unit of velocity (that is to say, using the unit of force 

 selected according to the system of Gauss, and which is often called the 

 " absolute " or the " kinetic " unit of force *), and taking water-pressures 

 as being reckoned from the atmospheric pressure as zero, let 



p = density of the water ; 

 V = velocity at U ; 

 /ij= pressure-height at B, or the height of a column of statical water 



which would produce the pressure at B ; 

 h = pressure-height at U ; 

 ^j= pressure in units of force per unit of area at B ; 

 /)= pressure in units of force per unit of area at TJ ; 

 / = fall from B to U, measured vertically ; 



5 = fall of free level in the flow from the region of statical water to U ; 

 then 



and 



p=gph. 



Let a small mass, m, of the water, whose volume (or content voluminally 

 considered) is denoted by c, be introduced into the stream, its first place 

 being at B just outside of the initial interface B' B B", and let it flow forward 

 in the stream tiU it reaches a second place at U where it is just past the inter- 

 face U' XJ TJ". In the stream filament B U E the space between the two inter- 

 faces at B and TJ is traversed alike by both front and rear of the small mass 

 m ; and therefore no excess of energy is given or taken by the mass in conse- 

 quence of the pressure on its front and of that on its rear, for the passage 

 of its front from the interface at B to that at TJ, and of its rear over the 

 same space. 



* The units of force derivable by the method of Gauss from the various units of 

 length, mass, and time, in common use, though spoken of imder general designations such 

 as "absolute tmits of force" or "kinetic units of force," have until lately been individually 

 anonymous: and this deficiency, notwithstanding the important scientific and practical 

 uses which these units were capable of serving, has been a great hindrance and discou- 

 ragement to their general employment in dynamical investigations, aud even to any satis- 

 factory spread of knowledge of their meaning. Three years ago, the British- Association 

 Committee on Dynamical and Electrical Units (Brit. Assoc. Report, 1873, part I, p. 222), 

 taking the centimetre, the gram, and the second as units of length, mass, and time, 

 named the force so derived tlie Dyne. For the unit of force derived from the foot, 

 the pound, and the second, the name Powndal has been introduced by myself ; and it 

 seems likely to come into use. At this Meeting of the British Association I have proposed 

 the Crinal and the Funal as names for the two imits of force derived respectively, one 

 from the decimetre, the kilogram, and the second, and the other from the metre, the 

 tonne, and the second (see Proceedings of Section A in the present volume). The 

 familiarization of these important units to the minds of students of dynamics will, 

 in a very important degree, aid the acquisition of clear and true views in hydrokinetics, 

 as also in dynamics generally. 



